Compositions that are useful for cleaning various substrates often contain a wide variety of ingredients. U.S. Pat. No. 5,609,862 discloses compositions for cleaning hair that include polymer and anionic surfactant, among other ingredients. It is desired to provide laundry compositions that contain at least one polymer and at least one further ingredient such as at least one surfactant, at least one softening agent, or some mixture thereof. It is known in the art that certain ingredients are incompatible with each other; that is, combinations of those ingredients, when included in a laundry composition, cause some properties of the laundry composition (such as, for example, clarity, cleaning effectiveness, effectiveness at inhibiting clay soil redeposition, softening effectiveness, other properties, or combinations thereof) to become less desirable. It is desired to provide laundry compositions that are robust; that is, laundry compositions that can be formulated with combinations of some ordinarily incompatible ingredients without significant loss of desirable properties. For example, some of such desirable laundry compositions include both cationic softening agent and anionic surfactant; in the past, such compositions were not effective both at cleaning and at softening; it is desired to provide such laundry compositions that are effective at cleaning (in particular, at inhibiting clay soil redeposition) and at softening. For another example, some of such desirable laundry compositions include both cationic softening agent and anionic surfactant; in the past, such compositions exhibited turbidity or phase separation; it is also desired to provide such laundry compositions that do not phase separate and that have low turbidity. For yet another example, it is desired to provide laundry compositions that include at least one anionic surfactant, that may or may not also include a softening agent, and that provide better inhibition of clay soil redeposition than that provided by previously-known laundry compositions.